FANTASY: User-friendly Symplectic Geodesic Integrator for Arbitrary Metrics with Automatic Differentiation
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Affiliation
Astronomy Department, University of ArizonaData Science Institute, University of Arizona
Program in Applied Mathematics, University of Arizona
Issue Date
2021
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IOP Publishing LtdCitation
Christian, P., & Chan, C. K. (2021). FANTASY: User-friendly Symplectic Geodesic Integrator for Arbitrary Metrics with Automatic Differentiation. The Astrophysical Journal, 909(1), 67.Journal
Astrophysical JournalRights
Copyright © 2021 The American Astronomical Society. All rights reserved.Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.Abstract
We present FANTASY (Finally A Numerical Trajectory Algorithm both Straightforward and sYmplectic), a user-friendly, open-source symplectic geodesic integrator written in Python. FANTASY is designed to work "out of the box"and does not require anything from the user aside from the metric and the initial conditions for the geodesics. FANTASY efficiently computes derivatives up to machine precision using automatic differentiation, allowing the integration of geodesics in arbitrary space(times) without the need for the user to manually input Christoffel symbols or any other metric derivatives. Further, FANTASY utilizes a Hamiltonian integration scheme that doubles the phase space, where two copies of the particle phase space are evolved together. This technique allows for an integration scheme that is both explicit and symplectic, even when the Hamiltonian is not separable. FANTASY comes prebuilt with second- and fourth-order schemes, and is easily extendable to higher-order schemes. FANTASY also includes an automatic Jacobian calculator that allows for coordinate transformations to be done automatically. © 2021. The American Astronomical Society. All rights reserved..Note
Immediate accessISSN
0004-637XVersion
Final published versionae974a485f413a2113503eed53cd6c53
10.3847/1538-4357/abdc28